Fm-3m No. 225 F4/m-32/m Oh5


Axes Coordinates Wyckoff positions 
4a 4b 8c 24d 24e 32f 48g
48h 48i 96j 96k 192l
I Maximal translationengleiche subgroups
[2] F-43m 4a 4b 4c; 4d 24g 24f 2 × 16e 2 × 24g
  (216) 48h 48h 96i 2 × 48h 2 × 96i
[2] F432 4a 4b 8c 24d 24e 32f 48i
  (209) 48g 48h 96j 96j 2 × 96j
[2] Fm-3 4a 4b 8c 24d 24e 32f 48g
  (202) 48h 48h 2 × 48h 96i 2 × 96i
[4] R-3m (1/2)(b + c), (1/2)(a + c), -x + y + z, 1a 1b 2c 3d; 3e 6h 2c; 6h 2 × 6h
  (166) (1/2)(a + b) x - y + z, 6f; 6h 6g; 6h 2 × 12i 2 × 6h; 12i 4 × 12i
(rhombohedral axes) x + y - z
(1/2)(-a + b), (2/3)(-2x + y + z), 3a 3b 6c 9d; 9e 18h 6c; 18h 2 × 18h
(1/2)(-b + c), a + b + c (2/3)(-x - y + 2z), 18f; 18h 18g; 18h 2 × 36i 2 × 18h; 36i 4 × 36i
(hexagonal axes) (1/3)(x + y + z)
 conjugate: (1/2)(a + b), (1/2)(-b - c), (2/3)(2x + y - z),
-a + b - c (2/3)(x - y - 2z),
(hexagonal axes) (1/3)(-x + y - z)
 conjugate: (1/2)(-a - b), (1/2)(b - c), (2/3)(-2x - y - z),
a - b - c (2/3)(-x + y - 2z),
(hexagonal axes) (1/3)(x - y - z)
 conjugate: (1/2)(a - b), (1/2)(b + c), (2/3)(2x - y + z),
-a - b + c (2/3)(x + y + 2z),
(hexagonal axes) (1/3)(-x - y + z)
[3] I4/mmm (1/2)(a - b), (1/2)(a + b), c x - y, x + y, z 2a 2b 4d 4c; 8f 4e; 8h 16n 8g; 16k
  (139) 8i; 16m 8j; 16m 16l; 2 × 16m 16n; 32o 3 × 32o
 conjugate: (1/2)(b - c), (1/2)(b + c), a y - z, y + z, x
 conjugate: (1/2)(-a + c), (1/2)(a + c), b -x + z, x + z, y
II Maximal klassengleiche subgroups
   Loss of centring translations
[4] Pn-3m origin 1 : x + (1/4), y + (1/4), z + (1/4) 4b 4c 2a; 6d 12f; 12g 24k 8e; 24k 2 × 12g; 24h
  (224) origin 2: x, y, z 24i; 24k 24j; 24k 2 × 48l 2 × 24k; 48l 4 × 48l
4 conjugate subgroups
[4] Pm-3m 1a; 3c 1b; 3d 8g 12i; 12j 6e; 6f; 12h 8g; 24m 2 × 24m
  (221) 4 conjugate subgroups 2 × 12i; 24l 2 × 12j; 24k 2 × 24k; 2 × 24l 2 × 24m; 48n 4 × 48n
   Enlarged unit cell, isomorphic
[27] Fm-3m 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; 4a; 24e; 4b; 24e; 8c; 2 × 32f; 24d; 48g; 3 × 24e; 3 × 32f; 3 × 48g;
±((1/3), 0, 0); 32f; 48h 32f; 48i 48g; 96k 48h; 48i; 3 × 96j; 6 × 96k; 6 × 96k;
±(0, (1/3), 0); 96j; 2 × 96k; 3 × 96k 192l 3 × 192l
±(0, 0, (1/3)); 192l
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3));
±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); 3 × 48h; 3 × 48i; 9 × 96j; 9 × 96k; 27 × 192l
±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); 3 × 96j; 3 × 96j; 9 × 192l 9 × 192l
±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); 3 × 96k; 3 × 96k;
±((1/3), (2/3), (1/3)); ±((1/3), (1/3), (2/3)) 3 × 192l 3 × 192l


Axes Coordinates Wyckoff positions
  4a 4b 8c 24d 24e 32f
48g 48h 48i 96j 96k 192l
[p3] Fm-3m pa, pb, pc (1/p)x, (1/p)y, (1/p)z; 4a; ((p - 1)/2) × 24e; 4b; ((p - 1)/2) × 24e; 8c; (p - 1) × 32f; 24d; ((p - 1)/2) × 48g; p × 24e; p × 32f;
+((u/p), (v/p), (w/p)) ((p - 1)/2) × 32f; ((p - 1)/2) × 32f; ((p - 1)/2) × 48g; ((p - 1)/2) × 48h; ((p(p - 1))/2) × 96j; p(p - 1) × 96k;
p = prime > 2; ((p - 1)/2) × 48h; ((p - 1)/2) × 48i; (((p - 1)(p - 2))/2) × 96k; ((p - 1)/2) × 48i; ((p(p - 1))/2) × 96k; ((p(p - 1)(p - 2))/6) × 192l
u, v, w = 1, . . ., p - 1 (((p - 1)(p - 3))/8) × 96j; (((p - 1)(p - 3))/8) × 96j; (((p - 1)(p - 2)(p - 3))/24) × (((p - 1)2)/4) × 96j; ((p(p - 1)(p - 3))/8) ×
(((p - 1)(p - 3))/4) × 96k; (((p - 1)(p - 3))/4) × 96k; 192l (((p - 1)2)/2) × 96k; 192l
(((p - 1)(p - 3)(p - 5))/48) × (((p - 1)(p - 3)(p - 5))/48) × (((p - 1)3)/8) × 192l
192l 192l
p × 48g; p × 48h; p × 48i; p2 × 96j; p2 × 96k; p3 × 192l
p(p - 1) × 96k; ((p(p - 1))/2) × 96j; ((p(p - 1))/2) × 96j; ((p2(p - 1))/2) × 192l ((p2(p - 1))/2) × 192l
((p(p - 1)2)/4) × 192l ((p(p - 1))/2) × 96k; ((p(p - 1))/2) × 96k;
((p(p - 1)2)/4) × 192l ((p(p - 1)2)/4) × 192l









































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